NEW YORK, NY, USA -- No.13 seed Kiki Bertens of the Netherlands continued to demonstrate ferocious form during the hardcourt summer, claiming her eighth straight win with a 6-2, 6-1 victory over American qualifier Francesca Di Lorenzo at the US Open on Thursday.

Bertens won the biggest title of her career earlier this month at the Western & Southern Open in Cincinnati, defeating four Top 10 players en route, including World No.1 Simona Halep in the final. But this makes her first appearance in the third round of the US Open, on her eighth showing in the main draw in New York.

"This year, in all the Slams, I made the third round, so I think that’s pretty steady -- that’s not really a word I’ve used in the last few years!" Bertens exclaimed, during her post-match meeting with the media. "It feels great, to be honest, to reach here my first third-round, it’s unbelievable."

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"I think it’s belief and confidence, of course," Bertens said, regarding her newfound consistency at the Slams. "But I think it’s more that, before, I’d be stressed coming into a Grand Slam, like, ‘Okay, I have to play good, and I want to get my points here.’ I think that now, I’m a little bit more relaxed."

"I just try to play as good as I can, and if I lose, okay, there’s the next week again, so it doesn’t matter so much where you get your points," Bertens continued. "I don’t put so much pressure anymore on myself."

She exhibited more incredible form today against Di Lorenzo, who was making her Grand Slam main draw debut at this event. Bertens fired 18 winners, including five aces, which outpaced her 17 unforced errors. Di Lorenzo looked strong in her first-round victory over her compatriot Christina McHale on Tuesday, but was undone by 28 unforced errors against Bertens.

"I didn’t know my opponent, so that was a bit tough in the beginning," Bertens admitted. "I think she started pretty well. I was still searching a little bit, like how I wanted to play, but I think I was just solid today. Maybe not as big as I want to play, maybe not as aggressive, but I think it was a good tactic for today."

Kiki Bertens flashing a big smile after making 3R @usopen for the 1st time. Says the key to her Slam performances this year has been managing the stress and pressure she put on herself. Also well aware she’s in the hunt to qualify for @WTAFinalsSG. #USOpen

In other second round matches, 19-year-old Czech Marketa Vondrousova reached the third round at a Grand Slam event for the first time in her young career, taking out former World No.5 and 2014 Wimbledon finalist Eugenie Bouchard of Canada, 6-4, 6-3, in one hour and 20 minutes.

Vondrousova will play Bertens in the third round, and could be a difficult opponent for the Dutchwoman. The teenager won her first WTA title last year in Biel and cracked the Top 50 earlier this year, but has slid to a current ranking of World No.103 and was the last player to receive direct entry into the main draw.

However, the young Czech was able to ease past Bouchard, outpacing the Canadian in winners by 15 to 14, while Bouchard had 32 unforced errors, seven more than Vondrousova. Bouchard is also trying to rebuild her ranking, and is back within striking distance of the Top 100 after qualifying for the main draw at the US Open, and winning her opening match against French wild card Harmony Tan.

No.11 seed Daria Kasatkina of Russia has been the highest-profile upset of the day so far, losing to Belarusian Aliaksandra Sasnovich, 6-2, 7-6(3). Kasatkina was attempting to reach her third straight Grand Slam quarterfinal, having made the elite eight at both Roland Garros and Wimbledon, as she attempts to make her long-awaited Top 10 debut in the WTA rankings.

But Sasnovich is also rapidly improving her ranking having bolted up roughly 50 spots ever since reaching the Brisbane final in the first week of the season, currently sitting just outside the Top 30. Both players had an equal amount of unforced errors (33 apiece) but Sasnovich outdid the Russian in winners by a 21 to 14 margin.

Sasnovich will now face No.20 seed Naomi Osaka in the third round, after the Japanese No.1 quickly dispatched Israeli qualifier Julia Glushko, 6-2, 6-0, in 50 minutes. Indian Wells champion Osaka crushed 19 winners, to her opponent's six, and won two-thirds of the points on Glushko's second serve.

Additionally, the most recent WTA titlist, No.26 seed Aryna Sabalenka of Belarus, survived a tough battle with 2010 US Open finalist Vera Zvonareva of Russia, winning 6-3, 7-6(7). Sabalenka, who sits at a career-high No.20 after picking up the New Haven title on Saturday, saved a set point against her in the second-set tiebreak before moving past former World No.2 Zvonareva, who qualified for this year's main draw.